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Math Help - Implicit differentiation/ partial differentiation

  1. #1
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    Implicit differentiation/ partial differentiation

    How do i find the partial derivative in terms of Y from the equation z = x^y even if X is held as a constant i dont know how to differentiate it :S
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  2. #2
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    Actually, is the answer just zero?
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  3. #3
    Junior Member bondesan's Avatar
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    Post

    Follow these steps, where z_y means the derivative of z with respect of y.

    \displaystyle{z=x^y}

    \displaystyle{ln(z) = y\cdot ln(x)}

    \displaystyle{\frac{\partial}{\partial y} ln (z) = \frac{\partial}{\partial y}\left(y\cdot ln (x)\right)}

    \displaystyle{\frac{z_y}{z} = ln (x)}

    \displaystyle{z_y = z\cdot ln (x) = x^y\cdot ln (x)}

    Got it?
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